Evolution of Massive Black Hole Binaries

We present the result of large-scale N-body simulations of the stellar-dynamical evolution of a massive black-hole binary at the center of a spherical galaxy. We focus on the dependence of the hardening rate on the relaxation timescale of the parent galaxy. A simple theoretical argument predicts that a binary black hole creates the ``loss cone'' around it. Once the loss cone is formed, the hardening rate is determined by the rate at which field stars diffuse into the loss cone. Therefore the hardening timescale becomes proportional to the relaxation timescale. Recent N-body simulations, however, have failed to confirm this theory and various explanations have been proposed. By performing simulations with sufficiently large N (up to $10^6$) for sufficiently long time, we found that the hardening rate does depend on N. Our result is consistent with the simple theoretical prediction that the hardening timescale is proportional to the relaxation timescale. This dependence implies that most massive black hole binaries are unlikely to merge within the Hubble time through interaction with field stars and gravitational wave radiation alone.Comment: Reviced version accepted for publication in ApJ. Scheduled to appear in the February 10, 2004 issu

All Maximal Independent Sets and Dynamic Dominance for Sparse Graphs

We describe algorithms, based on Avis and Fukuda's reverse search paradigm, for listing all maximal independent sets in a sparse graph in polynomial time and delay per output. For bounded degree graphs, our algorithms take constant time per set generated; for minor-closed graph families, the time is O(n) per set, and for more general sparse graph families we achieve subquadratic time per set. We also describe new data structures for maintaining a dynamic vertex set S in a sparse or minor-closed graph family, and querying the number of vertices not dominated by S; for minor-closed graph families the time per update is constant, while it is sublinear for any sparse graph family. We can also maintain a dynamic vertex set in an arbitrary m-edge graph and test the independence of the maintained set in time O(sqrt m) per update. We use the domination data structures as part of our enumeration algorithms.Comment: 10 page

MYRIAD: A new N-body code for simulations of Star Clusters

We present a new C++ code for collisional N-body simulations of star clusters. The code uses the Hermite fourth-order scheme with block time steps, for advancing the particles in time, while the forces and neighboring particles are computed using the GRAPE-6 board. Special treatment is used for close encounters, binary and multiple sub-systems that either form dynamically or exist in the initial configuration. The structure of the code is modular and allows the appropriate treatment of more physical phenomena, such as stellar and binary evolution, stellar collisions and evolution of close black-hole binaries. Moreover, it can be easily modified so that the part of the code that uses GRAPE-6, could be replaced by another module that uses other accelerating-hardware like the Graphics Processing Units (GPUs). Appropriate choice of the free parameters give a good accuracy and speed for simulations of star clusters up to and beyond core collapse. Simulations of Plummer models consisting of equal-mass stars reached core collapse at t~17 half-mass relaxation times, which compares very well with existing results, while the cumulative relative error in the energy remained below 0.001. Also, comparisons with published results of other codes for the time of core collapse for different initial conditions, show excellent agreement. Simulations of King models with an initial mass-function, similar to those found in the literature, reached core collapse at t~0.17, which is slightly smaller than the expected result from previous works. Finally, the code accuracy becomes comparable and even better than the accuracy of existing codes, when a number of close binary systems is dynamically created in a simulation. This is due to the high accuracy of the method that is used for close binary and multiple sub-systems.Comment: 24 pages, 29 figures, accepted for publication to Astronomy & Astrophysic

Cluster Mass Estimate and a Cusp of the Mass Density Distribution in Clusters of Galaxies

We study density cusps in the center of clusters of galaxies to reconcile X-ray mass estimates with gravitational lensing masses. For various mass density models with cusps we compute X-ray surface brightness distribution, and fit them to observations to measure the range of parameters in the density models. The Einstein radii estimated from these density models are compared with Einstein radii derived from the observed arcs for Abell 2163, Abell 2218, and RX J1347.5-1145. The X-ray masses and lensing masses corresponding to these Einstein radii are also compared. While steeper cusps give smaller ratios of lensing mass to X-ray mass, the X-ray surface brightnesses estimated from flatter cusps are better fits to the observations. For Abell 2163 and Abell 2218, although the isothermal sphere with a finite core cannot produce giant arc images, a density model with a central cusp can produce a finite Einstein radius, which is smaller than the observed radii. We find that a total mass density profile which declines as $\sim r^{-1.4}$ produces the largest radius in models which are consistent with the X-ray surface brightness profile. As the result, the extremely large ratio of the lensing mass to the X-ray mass is improved from 2.2 to 1.4 for Abell 2163, and from 3 to 2.4 for Abell 2218. For RX J1347.5-1145, which is a cooling flow cluster, we cannot reduce the mass discrepancy.Comment: 23 pages, 10 figures, Latex, uses aasms4.sty, accepted for publication in ApJ, Part

Compton Echoes from Gamma-ray Bursts

Recent observations of gamma-ray bursts (GRBs) have provided growing evidence for collimated outflows and emission, and strengthened the connection between GRBs and supernovae. If massive stars are the progenitors of GRBs, the hard photon pulse will propagate in the pre-burst, dense environment. Circumstellar material will Compton scatter the prompt GRB radiation and give rise to a reflection echo. We calculate luminosities, spectra, and light curves of such Compton echoes in a variety of emission geometries and ambient gas distributions, and show that the delayed hard X-ray flash from a pulse propagating into a red supergiant wind could be detectable by Swift out to z~0.2. Independently of the gamma-ray spectrum of the prompt burst, reflection echoes will typically show a high-energy cutoff between m_ec^2/2 and m_ec^2 because of Compton downscattering. At fixed burst energy per steradian, the luminosity of the reflected echo is proportional to the beaming solid angle, Omega_b, of the prompt pulse, while the number of bright echoes detectable in the sky above a fixed limiting flux increases as Omega_b^{1/2}, i.e. it is smaller in the case of more collimated jets. The lack of an X-ray echo at one month delay from the explosion poses severe constraints on the possible existence of a lateral GRB jet in SN 1987A. The late r-band afterglow observed in GRB990123 is fainter than the optical echo expected in a dense red supergiant environment from a isotropic prompt optical flash. Significant MeV delayed emission may be produced through the bulk Compton (or Compton drag) effect resulting from the interaction of the decelerating fireball with the scattered X-ray radiation.Comment: LaTeX, 18 pages, 4 figures, revised version accepted for publication in the Ap

Thermodynamic equilibrium and its stability for Microcanonical systems described by the Sharma-Taneja-Mittal entropy

It is generally assumed that the thermodynamic stability of equilibrium state is reflected by the concavity of entropy. We inquire, in the microcanonical picture, on the validity of this statement for systems described by the bi-parametric entropy $S_{_{\kappa, r}}$ of Sharma-Taneja-Mittal. We analyze the ``composability'' rule for two statistically independent systems, A and B, described by the entropy $S_{_{\kappa, r}}$ with the same set of the deformed parameters. It is shown that, in spite of the concavity of the entropy, the ``composability'' rule modifies the thermodynamic stability conditions of the equilibrium state. Depending on the values assumed by the deformed parameters, when the relation $S_{_{\kappa, r}}({\rm A}\cup{\rm B})> S_{_{\kappa, r}}({\rm A})+S_{_{\kappa, r}}({\rm B})$ holds (super-additive systems), the concavity conditions does imply the thermodynamics stability. Otherwise, when the relation $S_{_{\kappa, r}}({\rm A}\cup{\rm B})<S_{_{\kappa, r}}({\rm A})+S_{_{\kappa, r}}({\rm B})$ holds (sub-additive systems), the concavity conditions does not imply the thermodynamical stability of the equilibrium state.Comment: 13 pages, two columns, 1 figure, RevTex4, version accepted on PR

Recoverin Regulates Light-dependent Phosphodiesterase Activity in Retinal Rods

The Ca2+-binding protein recoverin may regulate visual transduction in retinal rods and cones, but its functional role and mechanism of action remain controversial. We compared the photoresponses of rods from control mice and from mice in which the recoverin gene was knocked out. Our analysis indicates that Ca2+-recoverin prolongs the dark-adapted flash response and increases the rod's sensitivity to dim steady light. Knockout rods had faster Ca2+ dynamics, indicating that recoverin is a significant Ca2+ buffer in the outer segment, but incorporation of exogenous buffer did not restore wild-type behavior. We infer that Ca2+-recoverin potentiates light-triggered phosphodiesterase activity, probably by effectively prolonging the catalytic activity of photoexcited rhodopsin

Effect of growth conditions on optical properties of CdSe/ZnSe single quantum dots

In this work, we have investigated the optical properties of two samples of CdSe quantum dots by using submicro-photoluminescence spectroscopy. The effect of vicinal-surface GaAs substrates on their properties has been also assessed. The thinner sample, grown on a substrate with vicinal surface, includes only dots with a diameter of less than 10 nm (type A islands). Islands of an average diameter of about 16 nm (type B islands) that are related to a phase transition via a Stranski-Krastanow growth process are also distributed in the thicker sample grown on an oriented substrate. We have studied the evolution of lineshapes of PL spectra for these two samples by improving spatial resolution that was achieved using nanoapertures or mesa structures. It was found that the use of a substrate with the vicinal surface leads to the suppression of excitonic PL emitted from a wetting layer.Comment: 2pages, 2 figures, Proceedings of International Conference On Superlattices Nano-Structures And Nano-Devices, July, Toulouse, France, to appear in the special issue of Physica